3t=21
[tex]t = \frac{21}{3} \\ t = \frac{ \cancel{{21}}{{}^{\:\:\:7}}}{\cancel3} \\ t = 7 \: \: answer[/tex]
Determine the exact value of sin 30° tan 45° + tan 30° sin 60⁰
Answer:
1.
Step-by-step explanation:
1) if sin30=0.5; tan45=1; tan30=1/√3; sin60=√3/2, then
2) 0.5+0.5=1.
Pa help naman po sa math Salamat po
Answer: See the table below
========================================================
Explanation:
The first task is to sort the values from largest to smallest.
Doing so gets us this list
57, 51, 48, 46, 45, 44, 43, 41, 40, 39, 39, 38, 37, 36, 36, 35, 35, 34, 33, 32, 31, 29, 29, 28, 24, 21, 19, 18, 13, 8
Next, we look for values that are between 56 and 60. That would be the single value of 57. This means we have 1 tally mark for the first row and the frequency is 1.
After that, we look for values between 51 and 55. That would be the single value of 51. Like the previous row, we'll have a single tally and a frequency of 1.
The 46-50 group will have the values 48 and 46 in it, so we have two tally marks and a frequency of 2 for this row.
This process is continued until all the values are accounted for. Effectively you are sorting the values into the proper bins.
You should end up with the table below. The fourth column is optional. It helps show where all of the values are sorted (to help confirm we have the correct tallies and frequencies).
Challenge. The mean of two numbers is
28. Find the numbers if 3 times one of the
numbers equals half the other number.
Hint. The mean of x and y is (x + y)/2 =
1/2(x + y).
Answer:
8 and 48
Step-by-step explanation:
Here is how to find it mathematically
x = one number 6x = other number ( because 3x is 1/2 of x)
(x + 6x) /2 = 28
7x = 56
x = 8 then 6x = 48
A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feat tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
Answer:
308
Step-by-step explanation:
so to find how much a rectangular prisim is by
length * with* height
11* 7 * 12
= 924 cubic feet
and then we just divid by 3
=308
Contagious diseases can spread quickly. Suppose 3 people are ill during the first week of an epidemic, and each person who is ill spreads the disease to five people by the end of the next week. By the end of the 8th week of the epidemic, how many people have become ill?
Answer:
1875
Step-by-step explanation:
3x5 = 15
15x 5 = 75
75x 5 = 375
375 x 5 = 1875
1875 because at the end of the next week, which basically turns 8 weeks into 4, and the number of contaminants multiply by 5 each other week.
Is AABC™ADEF? If so, identify the similarity postulate or theorem that
applies.
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answer:
A. Similar - AA
Step-by-step explanation:
The AA similarity postulate states that two triangles are similar if they have two congruent corresponding angles.
The triangles in the picture have two corresponding congruent angles.
Similar triangles may or may not be congruent
The true statement is (a) Similar - AA
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
From the complete question, we have the following highlights about the triangles
The angles at points A and D are congruent (85 degrees)
The angles at points B and E are congruent (30 degrees)
This means that the triangles are similar.
The similarity theorem is the AA theorem i.e. Angle-Angle
Hence, the true statement is (a) Similar - AA
Read more about similar triangles at:
brainly.com/question/14285697
#SPJ2
identify each expression that represents the slope of a tangent to the curve y=1/(x+1) at any point (x,y).
Answer:
Step-by-step explanation:
lim 1 / (x + h +1) - 1 (x + 1)
x--> 0
lim -h/ (x + h +1)(x + 1)
x--> 0
lim -h/ (x^2 + 2x + hx + h + 1)
x--> 0
-1/ (x^2 + 2x + 1)
Find an equation of the plane passing through the points (1, 5, -3), (2, 5, -3) and (3, 5,2)
Answer:
[tex]y = 5[/tex].
Or, equivalently:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Step-by-step explanation:
Every plane in [tex]\mathbb{R}^{3}[/tex] could be represented with a vector equation of the form [tex]\vec{n}\, (\vec{r} - \vec{r}_{0}) = 0[/tex], where:
[tex]\vec{n}[/tex] is a vector normal to the plane (a normal vector), and [tex]\vec{r}_{0}[/tex] is the position vector of a point in the plane.Notice that in this question, the coordinates (and hence the position vectors) of the points in this plane are already given. For example, the position vector of the point [tex](1,\, 5,\, -3)[/tex] is the vector:
[tex]\begin{aligned}\vec{r}_{0} = \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\end{aligned}[/tex].
Specifically in [tex]\mathbb{R}^{3}[/tex], normal vectors of a plane could be found by:
finding two distinct directions parallel to that plane, and taking the cross product between the two directions.Subtracting position vectors of points in this plane from each other would give directions that are parallel to this plane:
[tex]\begin{aligned}\begin{bmatrix}2 \\ 5 \\ -3\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix}\end{aligned}[/tex].
[tex]\begin{aligned}\begin{bmatrix}3 \\ 5 \\ 2\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix}\end{aligned}[/tex].
The cross product between these two vectors in [tex]\mathbb{R}^{3}[/tex] would be:
[tex]\begin{aligned} \vec{n} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \times \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix} = & \begin{bmatrix}0 \times 5 - 0 \times 0 \\ 0 \times 2 - 1 \times 5\\ 1 \times 0 - 0 \times 2\end{bmatrix} = \begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix}\end{aligned}[/tex].
(Note that the cross product between other directions parallel to the plane might give other normal vectors that are parallel to the one in this example.)
Using the position vector of the point [tex](1,\, 5,\, -3)[/tex] as [tex]\vec{r}_{0}[/tex], one possible vector equation for this plane would be:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Expand the dot product and simplify to obtain a scalar equation for this plane:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \begin{bmatrix}x - 1 \\ y - 5 \\ z - (-3)\end{bmatrix} = 0\end{aligned}[/tex].
[tex]0\, (x - 1) + (-3)\, (y - 5) + 0\, (z - (-3)) = 0[/tex].
[tex](-3)\, (y - 5) = 0[/tex].
[tex]y = 5[/tex].
Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you’ll find out. Consider ΔABC, whose vertices are A(2, 1), B(3, 3), and C(1, 6); let line segment AC represent the base of the triangle.
Part A
Find the equation of the line passing through B and perpendicular to AC .
Answer:
[tex]y : \frac{1}{5} x + \frac{12}{5}[/tex]
Step-by-step explanation:
the slope of the line AC :
[tex]\frac{6-1}{1-2} = \frac{5}{-1} =-5[/tex]
Let y : mx + p be the equation of the line D passing through B and perpendicular to AC.
Where m is the slope and p is the y value of the y intercept point.
The line D is perpendicular to AC means the product of their slopes is −1
Therefore
(−5) × m = −1
Then
[tex]m=\frac{-1}{-5} =\frac{1}{5}[/tex]
We obtain, the equation of D is :
[tex]y : \frac{1}{5} x + p[/tex]
At this point ,we still need the value of p to get the full equation of D.
B(3, 3)∈ D
[tex]3=\frac{1}{5} \left( 3\right) +p[/tex]
[tex]\Longleftrightarrow p=3-\frac{3}{5} =\frac{12}{5} =2.4[/tex]
thus , the equation of D is :
[tex]y : \frac{1}{5} x + \frac{12}{5}[/tex]
Yes it's possible through matrix
Let's find out the area formula for our vertices
That's
[tex]\\ \rm\Rrightarrow \left|\begin{array}{ccc}\rm 2&\rm 1&\rm 1\\ \rm 3&\rm 3&\rm 1\\ \rm 1&\rm 6&\rm 1\end{array}\right|[/tex]
The determinant values modulus is the area
Slope of AC
m=6-1/1-2=-5Perpendicular lines have slopes negative reciprocal to each other
Slope of line B to AC =1/5So
Equation in point slope
y-3=1/5(x-3)y=1/5x-3/5+3y=1/5x+12/5Find x. (x+10)+(3x-5)+x=180
For a triangle
Tickets are $10 for adults, a, and $5 for students, s, and they expect that twice as many students as adults will attend Their goal is to earn $1,500 from ticket sales. Write a system of equations to model the ticket sales, assuming the student councll> meets their goal. Use the model to determine the number of adult tickets and student tickets they expect to sell. Show work.
Using a system of equations, it is found that they expect to sell 175 adult tickets and 350 student tickets.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Number of adults that attend.Variable s: Number of students that attend.They expect that twice as many students as adults will attend, hence:
s = 2a.
Their goal is to earn $1,500 from ticket sales, hence:
10a + 5s = 1500.
10a + 5(2a) = 1500.
20a = 1500.
a = 1500/20.
a = 175.
s = 2a = 2 x 175 = 350.
They expect to sell 175 adult tickets and 350 student tickets.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Divide the number 1080 into two parts with a ratio of 4: 1.
Answer: It breaks up into 864+216
Reason:
x = some positive real number
The ratio 4:1 scales up to 4x:1x, so we have two parts one is 4x and the other is 1x. Those two parts add up to 1080
4x+1x = 1080
5x = 1080
x = 1080/5
x = 216
We can then find 4x = 4*216 = 864
As a check: 864+216 = 1080, so the answer is confirmed.
53) Darryl wants to buy socks for $15.27. He
gives the cashier $20. What is his
change?
Answer:
$4.73
Step-by-step explanation:
just do 20 minus 15.27
Help -x/3 > 5
A. X<15
B. X > -15
C. X < -15
D. X > 15
Answer:
Steps
-x/3 >5
Multiply both sides by 3
3(-x/3)>5.3
Simplify
-X> 15
Multiply both sides by - 1 (reverse the inequality)
(-x)(-1)<15(-1)
Simplify
X< -15
so C is the answer
Select the correct answer.
1
Which number is the additive inverse of –10 1/4
O A.
0
Ang
OB.
10 1/4
oc. 4/41
OD. -4 1/10
Reset
Answer:
The additive inverse of the number -10 1/4 is +41/4
The additive inverse of any number is such a number added to the given number to get zero.
Let the additive inverse of the given number be "x", hence:
-10 1/4 + x = 0
x = 0 - (-10 1/4)
x = 10 1/4
x = 41/4
Hence the additive inverse of the number -10 1/4 is +41/4
The area of a parallelogram is the product of the base b and the height h. Identify the formula.
Answer:
b x h
Step-by-step explanation:
product of the base (b) and the height (h) just means b x h.
7th grade math perimeter!!! Help
Answer:30.28 cm^2
Step-by-step explanation: area of the rectangle = 6x4 = 24
area of semicircle -> (πr^2)/2
radius of semcircle = 4/2 = 2
area of this question semicricle = (π2^2)/2
= 6.28 (3 s.f.)
total area = 24+6.28 =30.28 cm^2
remember put units ^^
I can’t solve this problem
Answer:
f(-2) = -8f(-1) = -5f(0) = 0f(1) = 7Step-by-step explanation:
f(w) = [tex]w^{2}[/tex] + 6w
w = -2f(w) = f(-2) = [tex](-2)^{2}[/tex] + 6*(-2) = 4 - 12 = -8
w = -1f(w) = f(-1) = [tex](-1)^{2}[/tex] + 6*(-1) = 1 - 6 = -5
w = 0f(w) = f(0) = [tex]0^{2}[/tex] + 6*0 = 0 + 0 = 0
w = 1f(w) = f(1) = [tex]1^{2}[/tex] + 6*1 = 1 + 6 = 7
PLEASE HELP 10 POINTS!!
Answer:
I think its c but not really sure but ill calculate it if I ever had the chance
In which of the following expressions does the number 2 fill in the blank so that the equation is true? Select all that apply.
A) 5(___ + 4) = 10 + 20
B) 9(3 + ___) = 27 + 18
C) 3(2 + 5) = ___ + 15
D) ___(5 + 6) = 10 + 12
Answer:
except c all
Step-by-step explanation:
because
5(2+4)=10+20
30=30
9(3+2)=27+18
45=45
2(5+6)=10+12
22=22
Answer:
except c all
Step-by-step explanation:
because
5(2+4)=10+20
30=30
9(3+2)=27+18
45=45
2(5+6)=10+12
22=22
Question 2 of 40
If a population is.
a sample of the population could be
A. 6th grade students whose last name begins with "T"; all students
in 6th grade
B. people in the front row; the entire audience
C. all the people at the park; the kids on the playground
о
D. trees over 20 feet tall; the entire forest
All of these can be samples but the best example is 6th grade students whose last name begins with "T"; all students in 6th grade
What is a sample?A sample refers to a small portion of a population. Most samples are selected randomly to make sure the sample represents all the population but they can also be selected based on a specific criterium.
What is one example of a sample?One example of this concept is 6th grade students whose last name begins with "T"; all students in 6th grade because the student whose last name begins with "T" are a fraction of all the population. Moreover, they are more likely to represent all the population.
Learn more about sample in: https://brainly.com/question/11045407
#SPJ1
Simplify [2 x (10+5)] - 5
Answer:
25
Step-by-step explanation:
[2 x (10+5)] - 5
[2 x (15)] - 5
[30] - 5
25
You deposit $400 in an account earning 5% interest compounded annually. How much will you have in the account in 10 years?
Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The amount that will be in the account after 10 years is $651.56.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
The principal amount is $400 which is invested for a period of 10 years at an interest rate of 5% annually. Therefore, the amount in the account after 10 years will be,
[tex]A = P(1+ \dfrac{r}{n})^{nt}\\\\A = \$400 (1+ \dfrac{0.05}{1})^{1 \times 10})\\\\A=\$651.56[/tex]
Hence, the amount that will be in the account after 10 years is $651.56.
Learn more about Compound Interest:
https://brainly.com/question/25857212
#SPJ1
demand for a certain product is random. It has been estimated that the monthly demand of the product has a normal distribution with a mend of 390units. The unit price of product is ETB 25. Ordering cost is ETB 40 per order and inventory carrying cost is estimated to be 35 percent per year. Calculate economic order quantity (EOQ)
The economic order quantity of the product with the demand of 390 units is 1392.86 units.
What is an economic order quantity?This refers to an inventory management technique that helps make efficient inventory management decisions.
The formula for economic order quantity is [tex]\sqrt{2 * D * S / H}[/tex]
Given data
Demand = 390 units.
Unit price of product is ETB 25.
Ordering cost is ETB 40 per order
inventory carrying cost is estimated to be 35 percent per yer
EOQ = [tex]\sqrt{2*390*25/40*0.35}}[/tex]
EOQ = 19,500 / 14
EOQ = 1392.85714286
EOQ = 1392.86 units
Read more about economic order quantity
brainly.com/question/16024963
#SPJ1
Help please?????????
√343k please simplify this
Answer:
the answer of√343k is 18k
Find the vertex of the parabola y=x^2 + 5x + 10
The coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].
What is the vertex of a parabola?Vertex of the parabola is the point of intersection of symmetry axis of the parabola and the parabola itself.
The given equation of parabola is [tex]y=x^2 + 5x + 10[/tex].
To get the coordinates of vertex of this parabola, we have to write the equation of parabola in the standard form.
So, write the equation of parabola in its standard form as,
[tex]y=x^2 + 5x + 10\\y=x^2+2\times \dfrac{5}{2}x+\dfrac{25}{4}-\dfrac{25}{4}+10\\y=(x-\dfrac{5}{2})^2+\dfrac{15}{4}\\(y-\dfrac{15}{4})=(x-\dfrac{5}{2})^2[/tex]
The standard form of parabola is,
[tex]y-b=(x-a)^2[/tex] where (a, b) is the coordinate of the vertex.
So, by comparing the equations, the vertex of the parabola will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].
Therefore, the coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].
Learn more about vertex of parabola here:
https://brainly.com/question/20333425
#SPJ1
Which expression is not equivalent to −4x3+x2−6x+8?
The expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).
What is the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The expression given in the problem is
f(x)=-4x³+x²-6x+8
The option given as,
(1) x² (-4x+1)-2(3x-4)(2) x(-4x²- x + 6) + 8(3) -4x³ + (x - 2)(x - 4)(4) -4(x³ - 2) + x(x - 6)From the given expression, if we take out x from the first three terms, it looks like option 2.
f(x)=-4x³+x²-6x+8
f(x)=x(-4x²+x-6)+8
From the given expression, if the last three terms factored, it looks like option 3.
f(x)=-4x³+x²-6x+8
f(x)=-4x³+x^2-4x-2x+8
f(x)=-4x³+x(x-4)-2(x-4)
f(x)=-4x³+(x-4)(x-2)
Rearrange the given expression, and make it looks like option 4.
f(x)=-4x³+x²-6x+8
f(x)=-4x²+8+x²-6x
f(x)=-4(x³-2)+x(x-6)
Thus, the expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).
Learn more about the equivalent expression here;
https://brainly.com/question/2972832
#SPJ1
The right circular cylinder represented below has a base radius of
3 centimeters and a height of 12 centimeters.
12 cm
3 cm
the right circular cylinder in cubic
Answer:
108π
Step-by-step explanation:
volume of a cylinder = πr²h , where r = radius and h = height
given values
radius = 3height = 12==> plugging in given values into formula
V = πr²h
r = 3 , h = 12
V = π(3²)(12)
==> evaluate exponent
V = π(9)(12)
==> multiply 9 and 12
V = 108π
y
is directly proportional to
x
2
.
If
y
=
112
when
x
=
4
find
y
when
x
=
9
Answer:
252
Step-by-step explanation:
Hope this helped you, and have a good day! (Please tell me if the answer is incorrect and I will try and correct it as soon as possible)
